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SEMIFIELDS ARISING FROM IRREDUCIBLE SEMILINEAR TRANSFORMATIONS

  • WILLIAM M. KANTOR (a1) and ROBERT A. LIEBLER (a2)

Abstract

A construction of finite semifield planes of order n using irreducible semilinear transformations on a finite vector space of size n is shown to produce fewer than different nondesarguesian planes.

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Copyright

Corresponding author

For correspondence; e-mail: kantor@math.uoregon.edu

References

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[1]Dembowski, P., Finite Geometries (Springer, Berlin, 1968).
[2]Dempwolff, U., ‘Normalformen semilinearer operatoren’, Math. Semesterber. 46 (1999), 205214.
[3]Dempwolff, U., Private communication, 2008.
[4]Jacobson, N., ‘Pseudo-linear transformations’, Ann. Math. 38 (1943), 484507.
[5]Jha, V. and Johnson, N. L., ‘An analog of the Albert–Knuth theorem on the orders of finite semifields, and a complete solution to Cofman’s subplane problem’, Algebras Groups Geom. 6 (1989), 135.
[6]Kantor, W. M., ‘Finite semifields’, in: Finite Geometries, Groups, and Computation, Proc. Conf., Pingree Park, CO, September 2005 (eds. A. Hulpke et al.) (de Gruyter, Berlin, 2006), pp. 103114.
[7]Knuth, D. E., ‘Finite semifields and projective planes’, J. Algebra 2 (1965), 182217.
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Keywords

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SEMIFIELDS ARISING FROM IRREDUCIBLE SEMILINEAR TRANSFORMATIONS

  • WILLIAM M. KANTOR (a1) and ROBERT A. LIEBLER (a2)

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